The Bible is silent. Both were taken alive. Elijah will return to die. Enoch is a type of the believer alive at the rapture who will never taste death.
My assumption would be they went to Abe's place as well, awaiting their redemption. Of course, they're not there now.
@Jrock
John 3:13 And no man hath ascended up to heaven, but he that came down from heaven, even the Son of man which is in heaven.
1 Corinthians 15:50 Now this I say, brethren, that flesh and blood cannot inherit the kingdom of God; neither doth corruption inherit incorruption.
I believe Enoch and Elijah are the two witnesses for the first half of the great tribulation before they get killed, resurrected, and called up to Heaven as a special midway rapture event for those 2 (
Revelation 11:1-13 KJV ) Just as philip was transported by one place to another place by the Spirit, so I believe those two are being transported through time and place.
Acts 8:39 And when they were come up out of the water, the Spirit of the Lord caught away Philip, that the eunuch saw him no more: and he went on his way rejoicing. 40 But Philip was found at Azotus: and passing through he preached in all the cities, till he came to Caesarea.
As for Abraham's bosom which is also known as Paradise, after His ascension, it is now located in Heaven per Paul's
indirect testimony of the apostle John's visit to Paradise in the third heavens for him to receive His words for the Book of Revelation.
2 Corinthians 12:1It is not expedient for me doubtless to glory. I will come to visions and revelations of the Lord. 2 I knew a man in Christ above fourteen years ago, (whether in the body, I cannot tell; or whether out of the body, I cannot tell: God knoweth

such an one caught up to the third heaven. 3 And I knew such a man, (whether in the body, or out of the body, I cannot tell: God knoweth

4 How that he was caught up into paradise, and heard unspeakable words, which it is not lawful for a man to utter.